%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM836+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:41:46 PM UTC 2026
% Result : Theorem 0.08s 15.44s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 51 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 27 ~; 19 |; 7 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 48 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ~ less(vd203,vd204)
| ~ greater(vd203,vd204) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ~ less(vd203,vd204)
| ~ greater(vd203,vd204) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
! [Vd198,Vd199] :
( less(Vd199,Vd198)
<=> ? [Vd201] : Vd198 = vplus(Vd199,Vd201) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Vd193,Vd194] :
( greater(Vd194,Vd193)
<=> ? [Vd196] : Vd194 = vplus(Vd193,Vd196) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Vd120,Vd121] :
( ~ ? [Vd125] : Vd121 = vplus(Vd120,Vd125)
| ~ ? [Vd123] : Vd120 = vplus(Vd121,Vd123) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
( less(vd203,vd204)
& greater(vd203,vd204) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
greater(vd203,vd204),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
less(vd203,vd204),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [Vd198,Vd199] :
( ( ! [Vd201] : Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ( ? [Vd201] : Vd198 = vplus(Vd199,Vd201)
| ~ less(Vd199,Vd198) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
( ! [Vd198,Vd199] :
( ! [Vd201] : Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ! [Vd198,Vd199] :
( ? [Vd201] : Vd198 = vplus(Vd199,Vd201)
| ~ less(Vd199,Vd198) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( ! [Vd198,Vd199] :
( ! [Vd201] : Vd198 != vplus(Vd199,Vd201)
| less(Vd199,Vd198) )
& ! [Vd198,Vd199] :
( Vd198 = vplus(Vd199,sK0_skl(Vd199,Vd198))
| ~ less(Vd199,Vd198) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Vd201,sK0_skl(Vd199,Vd198))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( X1 = vplus(X0,sK0_skl(X0,X1))
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [Vd193,Vd194] :
( ( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ( ? [Vd196] : Vd194 = vplus(Vd193,Vd196)
| ~ greater(Vd194,Vd193) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
( ! [Vd193,Vd194] :
( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ! [Vd193,Vd194] :
( ? [Vd196] : Vd194 = vplus(Vd193,Vd196)
| ~ greater(Vd194,Vd193) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
( ! [Vd193,Vd194] :
( ! [Vd196] : Vd194 != vplus(Vd193,Vd196)
| greater(Vd194,Vd193) )
& ! [Vd193,Vd194] :
( Vd194 = vplus(Vd193,sK1_skl(Vd194,Vd193))
| ~ greater(Vd194,Vd193) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Vd196,sK1_skl(Vd194,Vd193))],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = vplus(X1,sK1_skl(X0,X1))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f31,plain,
! [Vd120,Vd121] :
( ! [Vd125] : Vd121 != vplus(Vd120,Vd125)
| ! [Vd123] : Vd120 != vplus(Vd121,Vd123) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( X1 != vplus(X0,X3)
| X0 != vplus(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f44,plain,
! [X0,X1,X2] : X0 != vplus(vplus(X0,X1),X2),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f47,plain,
vd204 = vplus(vd203,sK0_skl(vd203,vd204)),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f52,plain,
! [X0] : vd203 != vplus(vd204,X0),
inference(paramodulation,[status(thm)],[f47,f44]) ).
fof(f61,plain,
vd203 = vplus(vd204,sK1_skl(vd203,vd204)),
inference(resolution,[status(thm)],[f25,f14]) ).
fof(f62,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f61,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM836+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/15.42 % CPULimit : 300
% 0.08/15.42 % WCLimit : 300
% 0.08/15.42 % DateTime : Mon Sep 21 03:12:07 UTC 2026
% 0.08/15.43 % CPUTime :
% 0.08/15.43 % Drodi V4.1.1
% 0.08/15.44 % Refutation found
% 0.08/15.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/15.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/15.46 % Elapsed time: 0.027185 seconds
% 0.08/15.46 % CPU time: 0.066838 seconds
% 0.08/15.46 % Total memory used: 12.724 MB
% 0.08/15.46 % Net memory used: 12.697 MB
%------------------------------------------------------------------------------